Sobhraj, 73, who is currently serving a life sentence, was taken to hospital for tests, his lawyer and mother-in-law Sakuntala Thapa told the AFP news agency.
The ageing conman, who has been implicated in more than 20 killings, needs to have one of the valves in his heart replaced, said Jyotendra Sharma, director of Sahid Gangalal National Heart Centre, where the surgery will take place.
It is not clear whether Sobhraj will remain in hospital until the surgery or be returned to the prison clinic.
Thapa said a decision would be made later on Friday.
"I have requested the jail authority to keep him in doctor's observation for a week in hospital before the surgery," she said.
Sobhraj was taken to hospital in late May after suffering a heart attack and was diagnosed with a weak valve that needed to be corrected through surgery.
Plea to return to France
His lawyer said that Sobhraj wanted to return to France for the surgery, a plea that he also made in a rare telephone interview with the Indian Express newspaper earlier this week.
But prison doctor Kedar Narshingh KC said he thought Sobhraj, who also earned the nickname "The Serpent" for his repeated identity thefts and escapes from justice, was angling to get released from jail early.
"He is spreading rumours despite our intensive care and treatment. It is suspicious and could be a ploy to get released from the jail," said the doctor.
The French embassy in Kathmandu told AFP there were "no ongoing discussions regarding the transfer of Sobhraj to France" for treatment or to serve the remainder of his sentence.
Convicted for US tourist's murder
Sobhraj, a French citizen of Vietnamese and Indian parentage, was sentenced by a Nepal court in 2004 for the killing of US tourist Connie Joe Bronzich in 1975.
It was the first time he had been convicted of murder, despite being linked to string of poisonings, killings and robberies of backpackers across Asia.
Two of his victims were found wearing only bikinis.
The law first caught up with him in India in 1976, when he was jailed for culpable homicide -- a lesser charge than murder -- for poisoning a French tourist and killing an Israeli man.
He spent 21 years in jail in India's capital with a brief 22-day break in 1986 when he escaped by reportedly offering the guards cakes, biscuits and grapes laced with sleeping pills.
In 2014 he was handed a second life sentence in Nepal for the killing of Canadian backpacker Laurent Carriere.